Information on Result #1667794
Linear OOA(2199, 3857142, F2, 6, 13) (dual of [(3857142, 6), 23142653, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2199, 3857142, F2, 2, 13) (dual of [(3857142, 2), 7714085, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2199, 4718589, F2, 2, 13) (dual of [(4718589, 2), 9436979, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2197, 4718588, F2, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(258, 524287, F2, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 59, 524287)-net over F2, using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, using
- linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- linear OOA(258, 524287, F2, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2197, 4718588, F2, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2199, 3857141, F2, 7, 13) (dual of [(3857141, 7), 26999788, 14]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(2199, 3857141, F2, 8, 13) (dual of [(3857141, 8), 30856929, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(2199, 3857141, F2, 18, 13) (dual of [(3857141, 18), 69428339, 14]-NRT-code) | [i] | ||